a correlation of mathematical models - pearson...

A Correlation of

Mathematical Models with Applications

Texas Edition, ©2015

To the Texas Essential Knowledge and Skills (TEKS)

for Mathematical Models with Applications

and the Texas English Language Proficiency Standards (ELPS)

Chapter 111. Mathematics §111.43. Mathematical Models with Applications, Adopted 2012 (One-Half to One Credit). Proclamation 2015

Page 1 of 205 Pearson Education, Inc., publishing as Prentice Hall: 9781269614115 Student Material

SubjectSubchapterCoursePublisherProgram TitleProgram ISBN 9781269614115

(a) General requirements. Students can be awarded one-half to one credit for successful completion of this course. Prerequisite: Algebra I. This course must be taken before receiving credit for Algebra II.

(b) Introduction.

(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.

(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

(3) Mathematical Models with Applications is designed to build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I. This mathematics course provides a path for students to succeed in Algebra II and prepares them for various post-secondary choices. Students learn to apply mathematics through experiences in personal finance, science, engineering, fine arts, and social sciences. Students use algebraic, graphical, and geometric reasoning to recognize patterns and structure, model information, solve problems, and communicate solutions. Students will select from tools such as physical objects; manipulatives; technology, including graphing calculators, data collection devices, and computers; and paper and pencil and from methods such as algebraic techniques, geometric reasoning, patterns, and mental math to solve problems.

Mathematical Models with Applications, Texas Edition

Correlations to the Texas Essential Knowledge and Skills (TEKS): Student Material

Chapter 111. MathematicsSubchapter C. High School§111.43. Mathematical Models with Applications, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice Hall



Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location

(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(A) apply mathematics to problems arising in everyday life, society, and the workplace

(i) apply mathematics to problems arising in everyday life Instruction 9781269614115 256 Activity 1

Review 9781269614115 352 Exercise 15



(ii) apply mathematics to problems arising in society

Instruction 9781269614115 80 Activity 1

Activity 9781269614115 31 Exercise 4

(4) In Mathematical Models with Applications, students will use a mathematical modeling cycle to analyze problems, understand problems better, and improve decisions. A basic mathematical modeling cycle is summarized in this paragraph. The student will: (A) represent: (i) identify the variables in the problem and select those that represent essential features; and (ii) formulate a model by creating and selecting from representations such as geometric, graphical, tabular, algebraic, or statistical that describe the relationships between the variables; (B) compute: analyze and perform operations on the relationships between the variables to draw conclusions; (C) interpret: interpret the results of the mathematics in terms of the original problem; (D) revise: confirm the conclusions by comparing the conclusions with the problem and revising as necessary; and (E) report: report on the conclusions and the reasoning behind the conclusions.

(5) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.

(c) Knowledge and Skills.






(iii) apply mathematics to problems arising in the workplace Instruction 9781269614115 131 Activity 6



(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution

(i) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process

Instruction 9781269614115 2 Activity 4, Steps in the Problem - Solving Process




(ii) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the reasonableness of the solution


Activity 9781269614115 17-20 Exercises 1-10





(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

(i) select tools, including real objects as appropriate, to solve problems

Instruction 9781269614115 757 Measuring Angles




(ii) select tools, including manipulatives as appropriate, to solve problems





(iii) select tools, including paper and pencil as appropriate, to solve problems

Instruction 9781269614115 17 Steps 1b, 2, and 3a







(iv) select tools, including technology as appropriate, to solve problems

Instruction 9781269614115 610 “Future Value Using Technology,”

Activity 9781269614115 623 Exercise 8bInstruction 9781269614115 789 Example 1



(v) select techniques, including mental math as appropriate, to solve problems

Instruction 9781269614115 91 Activity 2a




(vi) select techniques including estimation as appropriate, to solve problems

Instruction 9781269614115 176-177 Activity 2

Activity 9781269614115 175 Exercise 1b






(vii) select techniques, including number sense as appropriate, to solve problems


Activity 9781269614115 64 Exercise 9d


(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

(i) communicate mathematical ideas using multiple representations, including symbols as appropriate Instruction 9781269614115 14 “Formulas,”

Activity 9781269614115 9 Exercise 9cActivity 9781269614115 31 Exercise 4

Instruction 9781269614115 371 Example 1



(ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate Instruction 9781269614115 756 “How Big Is That Angle?” 2nd paragraph

Activity 9781269614115 33 Exercise 16Instruction 9781269614115 796 Activity 6a






(iii) communicate mathematical ideas using multiple representations, including graphs as appropriate Instruction 9781269614115 320 Activity 1b




(iv) communicate mathematical ideas using multiple representations, including language as appropriate Instruction 9781269614115 320 Activity 1c

Activity 9781269614115 554 Exercise 18f



(v) communicate mathematical reasoning using multiple representations, including symbols as appropriate Instruction 9781269614115 67-68 Defining Functions by a Symbolic Rule (Equation),

including Problem 4







(vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate Instruction 9781269614115 793 Activity 6a

Activity 9781269614115 786 Exercise 2a



(vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate Instruction 9781269614115 201 Activity 10




(viii) communicate mathematical reasoning using multiple representations, including language as appropriate Instruction 9781269614115 256 Activity 1a







(ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate Instruction 9781269614115 361 Delta Notation

Activity 9781269614115 731 Exercise 9e, 9f



(x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate Instruction 9781269614115 796 Activity 6a




(xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate Instruction 9781269614115 710-711 Activity 7







(xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate Instruction 9781269614115 254 Activity 3




(xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate Instruction 9781269614115 268 Activity 3 (2nd blue box)

Activity 9781269614115 726 Exercise 1c



(xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate Instruction 9781269614115 795-796 “Problem 3 demonstrates…” and Activity 6a







(xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate Instruction 9781269614115 201 Activity 10

Activity 9781269614115 214-215 Exercise 1b, 1d



(xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate Instruction 9781269614115 254 Activity 3



(E) create and use representations to organize, record, and communicate mathematical ideas

(i) create representations to organize mathematical ideas





(ii) create representations to record mathematical ideas

Instruction 9781269614115 703 Activity 9d







(iii) create representations to communicate mathematical ideas Instruction 9781269614115 359 Activity 1




(iv) use representations to organize mathematical ideas





(v) use representations to record mathematical ideas





(vi) use representations to communicate mathematical ideas Instruction 9781269614115 359 Activity 1






(F) analyze mathematical relationships to connect and communicate mathematical ideas

(i) analyze mathematical relationships to connect mathematical ideas Instruction 9781269614115 197 Activity 2




(ii) analyze mathematical relationships to communicate mathematical ideas Instruction 9781269614115 734 Activity 5c

Activity 9781269614115 744 Exercise 1aActivity 9781269614115 883 Exercise 12g

Instruction 9781269614115 933 Activity 10 (and sentences above it)


(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

(i) display mathematical ideas using precise mathematical language in written or oral communication





(ii) display mathematical arguments using precise mathematical language in written or oral communication

Instruction 9781269614115 734 Activity 7b

Activity 9781269614115 232 HCIP Exercise 6c






(iii) explain mathematical ideas using precise mathematical language in written or oral communication





(iv) explain mathematical arguments using precise mathematical language in written or oral communication





(v) justify mathematical ideas using precise mathematical language in written or oral communication Instruction 9781269614115 173 Activity 6




(vi) justify mathematical arguments using precise mathematical language in written or oral communication

Instruction 9781269614115 391 Activity 14f





(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:

(A) use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions

(i) use rates to solve problems involving personal finance Instruction 9781269614115 111 Activity 8




(ii) use rates to solve problems involving budgeting, including compensations Instruction 9781269614115 391 Activity 14




(iii) use rates to solve problems involving budgeting, including deductions Instruction 9781269614115 599 Activity 3

Activity 9781269614115 601 Problem 8



(iv) use linear functions to solve problems involving personal finance Instruction 9781269614115 604-605 Activity 6







(v) use linear functions to solve problems involving budgeting, including compensations Instruction 9781269614115 599 Activity 2




(vi) use linear functions to solve problems involving budgeting, including deductions Instruction 9781269614115 605 Activity 7



(B) solve problems involving personal taxes

(i) solve problems involving personal taxes




(C) analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees

(i) analyze data to make decisions about banking, including options for online banking Instruction 9781269614115 603 Online Banking…







(ii) analyze data to make decisions about banking, including checking accounts


Activity 9781269614115 462-463 Exercise 23



(iii) analyze data to make decisions about banking, including overdraft protection





(iv) analyze data to make decisions about banking, including processing fees


Activity 9781269614115 606–607 Exercise 1



(v) analyze data to make decisions about banking, including debit card/ATM fees Instruction 9781269614115 602 Activity 2





(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:

(A) use formulas to generate tables to display series of payments for loan amortizations resulting from financed purchases

(i) use formulas to generate tables to display series of payments for loan amortizations resulting from financed purchases




(B) analyze personal credit options in retail purchasing and compare relative advantages and disadvantages of each option

(i) analyze personal credit options in retail purchasing

Instruction 9781269614115 646 Open - ended Installment Loans




(ii) compare relative advantages of each option


Review 9781269614115 680 Exercise 7c



(iii) compare relative disadvantages of each option Instruction 9781269614115 640 Activity 5

Activity 9781269614115 629 Exercise 3cActivity 9781269614115 630 Exercise 6





(C) use technology to create amortization models to investigate home financing and compare buying a home to renting a home

(i) use technology to create amortization models to investigate home financing Instruction 9781269614115 631-632 Calculating the Monthly Mortgage Payment (below

Example 1)




(ii) use technology to create amortization models to compare buying a home to renting a home Instruction 9781269614115 640 Activity 4

Review 9781269614115 641 Exercise 6a


(D) use technology to create amortization models to investigate automobile financing and compare buying a vehicle to leasing a vehicle

(i) use technology to create amortization models to investigate automobile financing Instruction 9781269614115 626 Activity 3




(ii) use technology to create amortization models to compare buying a vehicle to leasing a vehicle Instruction 9781269614115 627 Activity 5





(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:

(A) analyze and compare coverage options and rates in insurance

(i) analyze coverage options in insurance





(ii) analyze coverage rates in insurance





(iii) compare coverage options in insurance





(iv) compare coverage rates in insurance







(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans

(i) investigate investment options, including stocks

Instruction 9781269614115 659-660 Stocks, Example 1




(ii) investigate investment options, including bonds

Instruction 9781269614115 661-663 Bonds, Example 2




(iii) investigate investment options, including annuities

Instruction 9781269614115 617 Definition




(iv) investigate investment options, including certificates of deposit Instruction 9781269614115 612 Activity 6

Activity 9781269614115 671 HCIP Exercise 1






(v) investigate investment options, including retirement plans Instruction 9781269614115 617 Paragraph 1




(vi) compare investment options, including stocks

Instruction 9781269614115 659-660 Example 1




(vii) compare investment options, including bonds





(viii) compare investment options, including annuities

Instruction 9781269614115 618 Activity 2e







(ix) compare investment options, including certificates of deposit Instruction 9781269614115 668 Activity 2




(x) compare investment options, including retirement plans Instruction 9781269614115 617 Paragraph 1



(C) analyze types of savings options involving simple and compound interest and compare relative advantages of these options

(i) analyze types of savings options involving simple interest Instruction 9781269614115 608 Activity 1




(ii) analyze types of savings options involving compound interest Instruction 9781269614115 608- 609 "Compound Interest" including Activity 3







(iii) compare relative advantages of these options


Activity 9781269614115 669 WHIL Exercise 2

(5) Mathematical modeling in science and engineering. The student applies mathematical processes with algebraic techniques to study patterns and analyze data as it applies to science. The student is expected to:

(A) use proportionality and inverse variation to describe physical laws such as Hook's Law, Newton's Second Law of Motion, and Boyle's Law

(i) use proportionality to describe physical laws





(ii) use inverse variation to describe physical laws




(B) use exponential models available through technology to model growth and decay in areas, including radioactive decay

(i) use exponential models available through technology to model growth in areas Instruction 9781269614115 740-741 Bird Flu (particularly Activity 4)

Review 9781269614115 739 Exercise 7






(ii) use exponential models available through technology to model decay in areas, including radioactive decay Instruction 9781269614115 702-703 Activity 8



(C) use quadratic functions to model motion

(i) use quadratic functions to model motion

Instruction 9781269614115 507-509 Activity 4.2 (Problems 1-5 and Quadratic Functions)

Activity 9781269614115 541 Exercise 1a - c

(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:

(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture

(i) use similarity to describe mathematical patterns in architecture


Activity 9781269614115 882 Exercises 11e-gActivity 9781269614115 900 Exercise 11

Instruction 9781269614115 865 Activities 5f and 5gInstruction 9781269614115 946 Activity 14c



(ii) use similarity to describe mathematical structure in architecture








(iii) use geometric transformations to describe mathematical patterns in architecture Instruction 9781269614115 901 Paragraph 1




(iv) use geometric transformations to describe mathematical structure in architecture Instruction 9781269614115 901 Paragraph 1




(v) use symmetry to describe mathematical patterns in architecture


Activity 9781269614115 766 Exercise 3Activity 9781269614115 915 Exercise 16



(vi) use symmetry to describe mathematical structure in architecture








(vii) use perspective drawings to describe mathematical patterns in architecture Instruction 9781269614115 946-947 Activity 14

Activity 9781269614115 976 Exercise 4Activity 9781269614115 980-982 Exercise 14



(viii) use perspective drawings to describe mathematical structure in architecture Instruction 9781269614115 946-947 Activity 14



(B) use scale factors with two-dimensional and three-dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields

(i) use scale factors with two-dimensional objects

Instruction 9781269614115 876 Activities 18 and 19







(ii) use scale factors with three-dimensional objects to demonstrate proportional changes in surface area as applied to fields Instruction 9781269614115 946 Activity 14d




(iii) use scale factors with three-dimensional objects to demonstrate proportional changes in volume as applied to fields Instruction 9781269614115 877 Paragraph below 21e

Activity 9781269614115 936 Exercise 8a – dActivity 9781269614115 980 Exercises 12 and 13

Instruction 9781269614115 932-934 Activities 9 and 11a



(iv) use scale factors with three-dimensional objects to demonstrate non-proportional changes in surface area as applied to fields

Instruction 9781269614115 889-890 Activities 6, 7, 8

Activity 9781269614115 947 Problem 16a-bInstruction 9781269614115 944 Activity 3






(v) use scale factors with three-dimensional objects to demonstrate non-proportional changes in volume as applied to fields Instruction 9781269614115 877 Paragraph below 21e

Activity 9781269614115 935 Exercise 2Instruction 9781269614115 944 Activity 5Instruction 9781269614115 947-948 Activity 16c-f


(C) use the Pythagorean Theorem and special right-triangle relationships to calculate distances

(i) use the Pythagorean Theorem to calculate distances

Instruction 9781269614115 895-896 Activity 6b

Activity 9781269614115 834 Exercise 6a977 Exercise 5



(ii) use special right-triangle relationships to calculate distances




(D) use trigonometric ratios to calculate distances and angle measures as applied to fields

(i) use trigonometric ratios to calculate distances as applied to fields





Activity 9781269614115 780 Exercises 10 and 11



(ii) use trigonometric ratios to calculate angle measures as applied to fields



(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:

(A) use trigonometric ratios and functions available through technology to model periodic behavior in art and music

(i) use trigonometric ratios available through technology to model periodic behavior in art Instruction 9781269614115 957 Activity 19

Activity 9781269614115 924 HCIP Exercise 16Activity 9781269614115 961 Exercise 10



(ii) use trigonometric ratios available through technology to model periodic behavior in music Instruction 9781269614115 827 Activity 10 and sentences above

Activity 9781269614115 820 Exercise 10832 WHIL Exercise 9



(iii) use trigonometric functions available through technology to model periodic behavior in art Instruction 9781269614115 955-957 “The Art in Trigonometry” and Activities 15-19







(iv) use trigonometric functions available through technology to model periodic behavior in music Instruction 9781269614115 827 Activities 10 and 12



(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography

(i) use similarity to describe mathematical patterns in art


Activity 9781269614115 898 Exercise 4Instruction 9781269614115 950 Activity 4



(ii) use similarity to describe mathematical patterns in photography

Instruction 9781269614115 893 Intro paragraph and definition

Activity 9781269614115 899 Exercises 8 and 9Instruction 9781269614115 894-895 Activity 3






(iii) use similarity to describe mathematical structure in art





(iv) use similarity to describe mathematical structure in photography

Instruction 9781269614115 893 Paragraph 1

Activity 9781269614115 899 Exercises 8 and 9Activity 9781269614115 948 Activity 17



(v) use geometric transformations to describe mathematical patterns in art


Activity 9781269614115 913-914 Exercises 8, 9, 12-15Activity 9781269614115 924 HCIP Exercises 15 and 16




(vi) use geometric transformations to describe mathematical patterns in photography Instruction 9781269614115 904 Activity 3

Activity 9781269614115 914 Exercises 10, 11




Activity 9781269614115 916 Exercises 17Instruction 9781269614115 910 Activity 11



(vii) use geometric transformations to describe mathematical structure in art


Activity 9781269614115 914-915, 924 Exercises 12 and 14Activity 9781269614115 914-915, 924 HCIP Exercise 16




(viii) use geometric transformations to describe mathematical structure in photography Instruction 9781269614115 904-905 Activity 3

Activity 9781269614115 914 Exercises 10Activity 9781269614115 916 Exercise 17




(ix) use symmetry to describe mathematical patterns in art

Instruction 9781269614115 910 Activity 10 (and paragraph below it)

Activity 9781269614115 912-915 Exercises 6, 9 12-14Activity 9781269614115 924 HCIP Exercise 15






(x) use symmetry to describe mathematical patterns in photography

Instruction 9781269614115 910 Activity 11 (and paragraph above it)




(xi) use symmetry to describe mathematical structure in art


Activity 9781269614115 912-915 Exercises 6, 9, 12, and 14cActivity 9781269614115 924 HCIP Exercise 15



(xii) use symmetry to describe mathematical structure in photography





(xiii) use perspective drawings to describe mathematical patterns in art


Activity 9781269614115 960-961 Exercise 7 and 10






(xiv) use perspective drawings to describe mathematical patterns in photography Instruction 9781269614115 954-955 Activities 11-14

Activity 9781269614115 960-961 Exercises 8 and 9



(xv) use perspective drawings to describe mathematical structure in art





(xvi) use perspective drawings to describe mathematical structure in photography Instruction 9781269614115 954-955 Activities 11-14

Activity 9781269614115 916 Exercise 17Activity 9781269614115 960 Exercises 8





(C) use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music

(i) use geometric transformations to describe mathematical patterns in music Instruction 9781269614115 910-911 Activities 12-14




(ii) use geometric transformations to describe mathematical structure in music Instruction 9781269614115 825 Activity 3




(iii) use proportions to describe mathematical patterns in music Instruction 9781269614115 825 Activity 3




(iv) use proportions to describe mathematical structure in music Instruction 9781269614115 826 Activity 4







(v) use periodic motion to describe mathematical patterns in music Instruction 9781269614115 827 Activity 9




(vi) use periodic motion to describe mathematical structure in music Instruction 9781269614115 827 Activity 9



(D) use scale factors with two-dimensional and three-dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields



Activity 9781269614115 960 Exercise 6Instruction 9781269614115 948 Activity17



(ii) use scale factors with three-dimensional objects to demonstrate proportional changes in surface area as applied to fields Instruction 9781269614115 876-877 Activity 21





Activity 9781269614115 882-883 Exercise 12Activity 9781269614115 963 WHIL Exercise 5

Instruction 9781269614115 932-934 Activity 9, Activity 11



(iii) use scale factors with three-dimensional objects to demonstrate proportional changes in volume as applied to fields Instruction 9781269614115 931-933 Activities 8 and 9









(v) use scale factors with three-dimensional objects to demonstrate non-proportional changes in volume as applied to fields Instruction 9781269614115 931-933 Activities 8 and 9





(8) Mathematical modeling in social sciences. The student applies mathematical processes to determine the number of elements in a finite sample space and compute the probability of an event. The student is expected to:

(A) determine the number of ways an event may occur using combinations, permutations, and the Fundamental Counting Principle

(i) determine the number of ways an event may occur using combinations Instruction 9781269614115 305-306 Combinations




(ii) determine the number of ways an event may occur using permutations Instruction 9781269614115 304 Activity 2




(iii) determine the number of ways an event may occur using the Fundamental Counting Principle Instruction 9781269614115 280 Activity 1 (Option 3)



(B) compare theoretical to empirical probability

(i) compare theoretical to empirical probability







(C) use experiments to determine the reasonableness of a theoretical model such as binomial or geometric

(i) use experiments to determine the reasonableness of a theoretical model



(9) Mathematical modeling in social sciences. The student applies mathematical processes and mathematical models to analyze data as it applies to social sciences. The student is expected to:

(A) interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, dot plots, stem-and-leaf plots, and box and whisker plots, to draw conclusions from the data and determine the strengths and weaknesses of conclusions

(i) interpret information from various graphs, including line graphs, to draw conclusions from the data





(ii) interpret information from various graphs, including bar graphs, to draw conclusions from the data








(iii) interpret information from various graphs, including circle graphs, to draw conclusions from the data

Instruction 9781269614115 191 Circle Graphs




(iv) interpret information from various graphs, including histograms, to draw conclusions from the data


Activity 9781269614115 318 Exercise 6b- c






(v) interpret information from various graphs, including scatterplots, to draw conclusions from the data


Activity 9781269614115 490 Exercise 12d, 12e



(vi) interpret information from various graphs, including dot plots, to draw conclusions from the data








(vii) interpret information from various graphs, including stem-and-leaf plots, to draw conclusions from the data





(viii) interpret information from various graphs, including box and whisker plots, to draw conclusions from the data








(ix) determine the strengths of conclusions

Instruction 9781269614115 172 Activity 3c




(x) determine the weaknesses of conclusions




(B) analyze numerical data using measures of central tendency (mean, median, and mode) and variability (range, interquartile range or IQR, and standard deviation) in order to make inferences with normal distributions

(i) analyze numerical data using measures of central tendency (mean, median, and mode) in order to make inferences with normal distributions

Instruction 9781269614115 210 Measures of Central Tendency







(ii) analyze variability (range, interquartile range or IQR, and standard deviation) in order to make inferences with normal distributions Instruction 9781269614115 322 Activity 3



(C) distinguish the purposes and differences among types of research, including surveys, experiments, and observational studies

(i) distinguish the purposes of research, including surveys Instruction 9781269614115 244 Paragraph 1 and below Highway Proposal




(ii) distinguish the purposes of research, including experiments Instruction 9781269614115 258 Activity 5

Activity 9781269614115 265 WHIL Exercise 5b



(iii) distinguish the purposes of research, including observational studies Instruction 9781269614115 259 Observational Study







(iv) distinguish the differences among types of research, including surveys Instruction 9781269614115 244-245 Opening paragraph and Highway Proposal Activities 1-3




(v) distinguish the differences among types of research, including experiments Instruction 9781269614115 258 Activity 5




(vi) distinguish the differences among types of research, including observational studies Instruction 9781269614115 259 Activity 7c

Activity 9781269614115 264 WHIL Exercise 5a


(D) use data from a sample to estimate population mean or population proportion

(i) use data from a sample to estimate population mean or population proportion Instruction 9781269614115 209 Activity 1






(E) analyze marketing claims based on graphs and statistics from electronic and print media and justify the validity of stated or implied conclusions

(i) analyze marketing claims based on graphs from electronic media





(ii) analyze marketing claims based on graphs from print media





(iii) analyze marketing claims based on statistics from electronic media


Review 9781269614115 358 Exercise 40



(iv) analyze marketing claims based on statistics from print media





Review 9781269614115 358 Exercise 39Activity 9781269614115 615 Exercise 6



(v) justify the validity of stated or implied conclusions




(F) use regression methods available through technology to model linear and exponential functions, interpret correlations, and make predictions

(i) use regression methods available through technology to model linear functions Instruction 9781269614115 420 Activity 5




(ii) use regression methods available through technology to model exponential functions Instruction 9781269614115 741 Activity 4




(iii) use regression methods available through technology to interpret correlations Instruction 9781269614115 423-424 Activity 9




Activity 9781269614115 429 Exercise 5e



(iv) use regression methods available through technology to make predictions Instruction 9781269614115 421 Activity 7b

Activity 9781269614115 490 Exercise 12e, 12g

(10) Mathematical modeling in social sciences. The student applies mathematical processes to design a study and use graphical, numerical, and analytical techniques to communicate the results of the study. The student is expected to:

(A) formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions

(i) formulate a meaningful question





(ii) determine the data needed to answer the question








(iii) gather the appropriate data





(iv) analyze the data

Instruction 9781269614115 253 Step 3




(v) draw reasonable conclusions







(B) communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation

(i) communicate methods used for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation





(ii) communicate analyses conducted for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation





(iii) communicate conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation




Page 52 of 205 Pearson Education, Inc., publishing as Prentice Hall: 9781269614115 Teacher Material

SubjectSubchapterCoursePublisherProgram TitleProgram ISBN

Mathematical Models with Applications, Texas Edition

Correlations to the Texas Essential Knowledge and Skills (TEKS): Teacher Material

Chapter 111. MathematicsSubchapter C. High School§111.43. Mathematical Models with Applications, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice Hall

9781269614115

(a) General requirements. Students can be awarded one-half to one credit for successful completion of this course. Prerequisite: Algebra I. This course must be taken before receiving credit for Algebra II.

(b) Introduction.

(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.

(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

(3) Mathematical Models with Applications is designed to build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I. This mathematics course provides a path for students to succeed in Algebra II and prepares them for various post-secondary choices. Students learn to apply mathematics through experiences in personal finance, science, engineering, fine arts, and social sciences. Students use algebraic, graphical, and geometric reasoning to recognize patterns and structure, model information, solve problems, and communicate solutions. Students will select from tools such as physical objects; manipulatives; technology, including graphing calculators, data collection devices, and computers; and paper and pencil and from methods such as algebraic techniques, geometric reasoning, patterns, and mental math to solve problems.






(i) apply mathematics to problems arising in everyday life Instruction 9781269614399 384 Activity 1




(ii) apply mathematics to problems arising in society


Review 9781269614399 357 Exercise 38

(4) In Mathematical Models with Applications, students will use a mathematical modeling cycle to analyze problems, understand problems better, and improve decisions. A basic mathematical modeling cycle is summarized in this paragraph. The student will: (A) represent: (i) identify the variables in the problem and select those that represent essential features; and (ii) formulate a model by creating and selecting from representations such as geometric, graphical, tabular, algebraic, or statistical that describe the relationships between the variables; (B) compute: analyze and perform operations on the relationships between the variables to draw conclusions; (C) interpret: interpret the results of the mathematics in terms of the original problem; (D) revise: confirm the conclusions by comparing the conclusions with the problem and revising as necessary; and (E) report: report on the conclusions and the reasoning behind the conclusions.

(5) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.

(c) Knowledge and Skills.






(iii) apply mathematics to problems arising in the workplace Instruction 9781269614399 98 Activity 1

Review 9781269614399 494-495 Exercise 26



(i) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process

Instruction 9781269614399 4 How to Solve It (gray box) and Problem 8




(ii) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the reasonableness of the solution


Activity 9781269614399 89 Exercise 6h






(i) select tools, including real objects as appropriate, to solve problems





(ii) select tools, including manipulatives as appropriate, to solve problems





(iii) select tools, including paper and pencil as appropriate, to solve problems








(iv) select tools, including technology as appropriate, to solve problems

Instruction 9781269614399 212 “Using Technology to Determine Measures of Central Tendency,"

Activity 9781269614399 215 Exercise 6Activity 9781269614399 216 Exercise 8a

Instruction 9781269614399 821-822 Problems 2-4



(v) select techniques, including mental math as appropriate, to solve problems





(vi) select techniques including estimation as appropriate, to solve problems


Activity 9781269614399 730 Exercise 8f-g






(vii) select techniques, including number sense as appropriate, to solve problems





(i) communicate mathematical ideas using multiple representations, including symbols as appropriate Instruction 9781269614399 67 Activity 3b

Activity 9781269614399 744 Exercise 1d-e



(ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate Instruction 9781269614399 791 Activity 6a







(iii) communicate mathematical ideas using multiple representations, including graphs as appropriate Instruction 9781269614399 202 Example 2




(iv) communicate mathematical ideas using multiple representations, including language as appropriate Instruction 9781269614399 314 Activity 14




(v) communicate mathematical reasoning using multiple representations, including symbols as appropriate Instruction 9781269614399 67-68 Defining Functions by a Symbolic Rule (Equation),

including Problem 4







(vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate Instruction 9781269614399 791 Activity 6a




(vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate Instruction 9781269614399 170-172 Activities 2 and 3




(viii) communicate mathematical reasoning using multiple representations, including language as appropriate Instruction 9781269614399 178 Activity 5a







(ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate Instruction 9781269614399 210 Measures of Central Tendency




(x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate Instruction 9781269614399 791 Activity 6a




(xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate Instruction 9781269614399 725 Activity 10







(xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate Instruction 9781269614399 178 Activity 5a




(xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate Instruction 9781269614399 219 Activity 9e




(xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate Instruction 9781269614399 791 Activity 6a







(xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate Instruction 9781269614399 173 Activity 6

Activity 9781269614399 727-728 Exercise 4 and 6c



(xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate Instruction 9781269614399 178 Activity 5a




(i) create representations to organize mathematical ideas





(ii) create representations to record mathematical ideas








(iii) create representations to communicate mathematical ideas Instruction 9781269614399 703 Activity 9




(iv) use representations to organize mathematical ideas





(v) use representations to record mathematical ideas





(vi) use representations to communicate mathematical ideas Instruction 9781269614399 314 Activity 14







(i) analyze mathematical relationships to connect mathematical ideas Instruction 9781269614399 198 Activity 5




(ii) analyze mathematical relationships to communicate mathematical ideas Instruction 9781269614399 314 Activity 14

Activity 9781269614399 868--869 Exercises 6b and 7



(i) display mathematical ideas using precise mathematical language in written or oral communication





(ii) display mathematical arguments using precise mathematical language in written or oral communication


Activity 9781269614399 232 HCIP Exercise 7b






(iii) explain mathematical ideas using precise mathematical language in written or oral communication





(iv) explain mathematical arguments using precise mathematical language in written or oral communication





(v) justify mathematical ideas using precise mathematical language in written or oral communication Instruction 9781269614399 181 Activity 7d

Activity 9781269614399 730 Exercise 8g



(vi) justify mathematical arguments using precise mathematical language in written or oral communication

Instruction 9781269614399 391 Activity 14f







(i) use rates to solve problems involving personal finance Instruction 9781269614399 100 Activity 7




(ii) use rates to solve problems involving budgeting, including compensations Instruction 9781269614399 599 Activity 1




(iii) use rates to solve problems involving budgeting, including deductions Instruction 9781269614399 600 Activity 5




(iv) use linear functions to solve problems involving personal finance Instruction 9781269614399 604-605 Activity 6







(v) use linear functions to solve problems involving budgeting, including compensations Instruction 9781269614399 391 Activity 14




(vi) use linear functions to solve problems involving budgeting, including deductions Instruction 9781269614399 605 Activity 7

(Drop-down menu) 9781269614399 607 Exercise 2


(B) solve problems involving personal taxes

(i) solve problems involving personal taxes





(i) analyze data to make decisions about banking, including options for online banking Instruction 9781269614399 603 Online Banking…







(ii) analyze data to make decisions about banking, including checking accounts





(iii) analyze data to make decisions about banking, including overdraft protection

Instruction 9781269614399 603 “Online Banking…”




(iv) analyze data to make decisions about banking, including processing fees

Instruction 9781269614399 603 “Online Banking…




(v) analyze data to make decisions about banking, including debit card/ATM fees Instruction 9781269614399 602 Activity 2






(A) use formulas to generate tables to display series of payments for loan amortizations resulting from financed purchases

(i) use formulas to generate tables to display series of payments for loan amortizations resulting from financed purchases





(i) analyze personal credit options in retail purchasing





(ii) compare relative advantages of each option





(iii) compare relative disadvantages of each option Instruction 9781269614399 640 Activity 5

Review 9781269614399 630 Exercise 6Review 9781269614399 680 Exercise 7c






(i) use technology to create amortization models to investigate home financing Instruction 9781269614399 632 Activity 3




(ii) use technology to create amortization models to compare buying a home to renting a home Instruction 9781269614399 625-626 “Calculating Amortization…”




(i) use technology to create amortization models to investigate automobile financing Instruction 9781269614399 625-626 “Calculating Amortization…”




(ii) use technology to create amortization models to compare buying a vehicle to leasing a vehicle Instruction 9781269614399 627-628 Activity 7







(i) analyze coverage options in insurance





(ii) analyze coverage rates in insurance





(iii) compare coverage options in insurance

Instruction 9781269614399 654 Permanent Life Insurance




(iv) compare coverage rates in insurance








(i) investigate investment options, including stocks





(ii) investigate investment options, including bonds

Instruction 9781269614399 661-663 Bonds, Example 2




(iii) investigate investment options, including annuities





(iv) investigate investment options, including certificates of deposit Instruction 9781269614399 612 Activity 6







(v) investigate investment options, including retirement plans Instruction 9781269614399 620-621 Activities 8 and 9




(vi) compare investment options, including stocks

Instruction 9781269614399 659 Stocks




(vii) compare investment options, including bonds





(viii) compare investment options, including annuities

Instruction 9781269614399 619-620 Present Value of an Annuity







(ix) compare investment options, including certificates of deposit Instruction 9781269614399 668 Activity 2




(x) compare investment options, including retirement plans Instruction 9781269614399 619-620 Present Value of an Annuity




(i) analyze types of savings options involving simple interest Instruction 9781269614399 604 Activity 5




(ii) analyze types of savings options involving compound interest Instruction 9781269614399 611 Activity 5







(iii) compare relative advantages of these options





(i) use proportionality to describe physical laws

Instruction 9781269614399 555 Activity 1 - 5 (together)




(ii) use inverse variation to describe physical laws





(i) use exponential models available through technology to model growth in areas Instruction 9781269614399 740-741 Bird Flu (Particularly Activity 4)







(ii) use exponential models available through technology to model decay in areas, including radioactive decay Instruction 9781269614399 702-703 Activity 8



(C) use quadratic functions to model motion

(i) use quadratic functions to model motion

Instruction 9781269614399 507-509 Activity 4.2 (Problems 1-5 and Quadratic Functions)

Activity 9781269614399 543 Exercise 3a - b



(i) use similarity to describe mathematical patterns in architecture



Instruction 9781269614399 865 Activities 5f and 5gInstruction 9781269614399 946 Activity 14c



(ii) use similarity to describe mathematical structure in architecture








(iii) use geometric transformations to describe mathematical patterns in architecture Instruction 9781269614399 901 Paragraph 1




(iv) use geometric transformations to describe mathematical structure in architecture Instruction 9781269614399 901 Paragraph 1




(v) use symmetry to describe mathematical patterns in architecture





(vi) use symmetry to describe mathematical structure in architecture








(vii) use perspective drawings to describe mathematical patterns in architecture Instruction 9781269614399 946-947 Activity 14




(viii) use perspective drawings to describe mathematical structure in architecture Instruction 9781269614399 946-947 Activity 14





Instruction 9781269614399 876 Activities 18 and 19







(ii) use scale factors with three-dimensional objects to demonstrate proportional changes in surface area as applied to fields Instruction 9781269614399 896 Activity 6b




(iii) use scale factors with three-dimensional objects to demonstrate proportional changes in volume as applied to fields Instruction 9781269614399 877 Paragraph below 21e

Activity 9781269614399 936 Exercises 8a-dActivity 9781269614399 980 Exercises 12 and 13

Instruction 9781269614399 932-934 Activities 9 and 11a




Instruction 9781269614399 889-890 Activities 6, 7, 8

Activity 9781269614399 947 Problem 16a-bInstruction 9781269614399 944 Activity 3






(v) use scale factors with three-dimensional objects to demonstrate non-proportional changes in volume as applied to fields Instruction 9781269614399 877 Paragraph below 21e

Activity 9781269614399 935 Exercise 2Instruction 9781269614399 944 Activity 5Instruction 9781269614399 947-948 Activity 16c-f



(i) use the Pythagorean Theorem to calculate distances





(ii) use special right-triangle relationships to calculate distances


Review 9781269614399 980-982 Exercise 14



(i) use trigonometric ratios to calculate distances as applied to fields








(ii) use trigonometric ratios to calculate angle measures as applied to fields





(i) use trigonometric ratios available through technology to model periodic behavior in art Instruction 9781269614399 957 Activity 19

Activity 9781269614399 924 HCIP Exercise 16Activity 9781269614399 961 Exercise 10



(ii) use trigonometric ratios available through technology to model periodic behavior in music Instruction 9781269614399 827 Activity 10 and sentences above

Activity 9781269614399 820 Exercise 10Activity 9781269614399 832 WHIL Exercise 9



(iii) use trigonometric functions available through technology to model periodic behavior in art

Instruction 9781269614399 955-957 “The Art in Trigonometry” and Activities 15-19







(iv) use trigonometric functions available through technology to model periodic behavior in music Instruction 9781269614399 827 Activity 10 and 12




(i) use similarity to describe mathematical patterns in art





(ii) use similarity to describe mathematical patterns in photography

Instruction 9781269614399 893 Intro paragraph and definition

Activity 9781269614399 899 Exercises 8 and 9Instruction 9781269614399 894-895 Activity 3






(iii) use similarity to describe mathematical structure in art





(iv) use similarity to describe mathematical structure in photography


Activity 9781269614399 899 Exercises 8 and 9Activity 9781269614399 948 Activity 17



(v) use geometric transformations to describe mathematical patterns in art


Activity 9781269614399 913-914 Exercises 8, 9, 12-15Activity 9781269614399 924 HCIP Exercises 15 and 16




(vi) use geometric transformations to describe mathematical patterns in photography Instruction 9781269614399 904 Activity 3








(vii) use geometric transformations to describe mathematical structure in art


Activity 9781269614399 914-915 Exercises 12 and 14Activity 9781269614399 924 HCIP Exercise 16




(viii) use geometric transformations to describe mathematical structure in photography Instruction 9781269614399 904 Activity 3





(ix) use symmetry to describe mathematical patterns in art

Instruction 9781269614399 910 Activity 10 (and paragraph below it)

Activity 9781269614399 912-915 Exercises 6, 9, 12-14Activity 9781269614399 924 HCIP Exercise 15






(x) use symmetry to describe mathematical patterns in photography

Instruction 9781269614399 910 Activity 11 (and paragraph above it)




(xi) use symmetry to describe mathematical structure in art


Activity 9781269614399 912-915 Exercises 6, 9, 12, and 14cActivity 9781269614399 924 HCIP Exercise 15



(xii) use symmetry to describe mathematical structure in photography





(xiii) use perspective drawings to describe mathematical patterns in art








(xiv) use perspective drawings to describe mathematical patterns in photography Instruction 9781269614399 954-955 Activities 11-14

Activity 9781269614399 960-961 Exercises 8 and 9



(xv) use perspective drawings to describe mathematical structure in art


Activity 9781269614399 959 Exercise 6 Activity 9781269614399 961 Exercise 10



(xvi) use perspective drawings to describe mathematical structure in photography Instruction 9781269614399 954-955 Activities 11-14

Activity 9781269614399 916 Exercise 17Activity 9781269614399 960 Exercises 8






(i) use geometric transformations to describe mathematical patterns in music Instruction 9781269614399 910-911 Activities 12-14




(ii) use geometric transformations to describe mathematical structure in music Instruction 9781269614399 825 Activity 3




(iii) use proportions to describe mathematical patterns in music Instruction 9781269614399 826 Activity 6




(iv) use proportions to describe mathematical structure in music Instruction 9781269614399 826 Activity 5







(v) use periodic motion to describe mathematical patterns in music Instruction 9781269614399 827 Activity 12




(vi) use periodic motion to describe mathematical structure in music Instruction 9781269614399 827 Activity 12





Instruction 9781269614399 865 Activity 5g

Activity 9781269614399 960 Exercise 6Instruction 9781269614399 948 Activity17



(ii) use scale factors with three-dimensional objects to demonstrate proportional changes in surface area as applied to fields Instruction 9781269614399 876-877 Activity 21

Activity 9781269614399 878-879 Exercise 1, Exercise 12




Activity 9781269614399 963 WHIL Exercise 5Instruction 9781269614399 932-934 Activity 9, Activity 11



(iii) use scale factors with three-dimensional objects to demonstrate proportional changes in volume as applied to fields Instruction 9781269614399 931-933 Activities 8 and 9









(v) use scale factors with three-dimensional objects to demonstrate non-proportional changes in volume as applied to fields Instruction 9781269614399 931-933 Activities 8 and 9







(i) determine the number of ways an event may occur using combinations Instruction 9781269614399 306 Formula Box




(ii) determine the number of ways an event may occur using permutations Instruction 9781269614399 304 Activity 1




(iii) determine the number of ways an event may occur using the Fundamental Counting Principle Instruction 9781269614399 280 Activity 1 (Option 3)



(B) compare theoretical to empirical probability

(i) compare theoretical to empirical probability







(C) use experiments to determine the reasonableness of a theoretical model such as binomial or geometric

(i) use experiments to determine the reasonableness of a theoretical model





(i) interpret information from various graphs, including line graphs, to draw conclusions from the data





(ii) interpret information from various graphs, including bar graphs, to draw conclusions from the data








(iii) interpret information from various graphs, including circle graphs, to draw conclusions from the data





(iv) interpret information from various graphs, including histograms, to draw conclusions from the data








(v) interpret information from various graphs, including scatterplots, to draw conclusions from the data

Instruction 9781269614399 421 Activity 7c

Activity 9781269614399 429 Exercise 5d, 5e



(vi) interpret information from various graphs, including dot plots, to draw conclusions from the data

Instruction 9781269614399 205 Summary 1

Activity 9781269614399 233 Exercise 8b, 8c






(vii) interpret information from various graphs, including stem-and-leaf plots, to draw conclusions from the data

Instruction 9781269614399 205 Summary 3




(viii) interpret information from various graphs, including box and whisker plots, to draw conclusions from the data








(ix) determine the strengths of conclusions





(x) determine the weaknesses of conclusions





(i) analyze numerical data using measures of central tendency (mean, median, and mode) in order to make inferences with normal distributions








(ii) analyze variability (range, interquartile range or IQR, and standard deviation) in order to make inferences with normal distributions Instruction 9781269614399 323 Activity 4b




(i) distinguish the purposes of research, including surveys Instruction 9781269614399 244 Paragraph 1 and below Highway Proposal




(ii) distinguish the purposes of research, including experiments Instruction 9781269614399 256 Paragraph 1




(iii) distinguish the purposes of research, including observational studies Instruction 9781269614399 259 Observational Study




Activity 9781269614399 264 WHIL Exercise 5a



(iv) distinguish the differences among types of research, including surveys Instruction 9781269614399 244-245 Opening paragraph and Highway Proposal Activities 1-3




(v) distinguish the differences among types of research, including experiments Instruction 9781269614399 259 Activity 7b




(vi) distinguish the differences among types of research, including observational studies Instruction 9781269614399 259 Activity 7a



(D) use data from a sample to estimate population mean or population proportion

(i) use data from a sample to estimate population mean or population proportion Instruction 9781269614399 211 Activity 9a







(i) analyze marketing claims based on graphs from electronic media





(ii) analyze marketing claims based on graphs from print media





(iii) analyze marketing claims based on statistics from electronic media


Review 9781269614399 358 Exercise 40



(iv) analyze marketing claims based on statistics from print media





Review 9781269614399 358 Exercise 39Activity 9781269614399 615 Exercise 6



(v) justify the validity of stated or implied conclusions





(i) use regression methods available through technology to model linear functions Instruction 9781269614399 420-421 Activity 6




(ii) use regression methods available through technology to model exponential functions Instruction 9781269614399 741 Activity 5c




(iii) use regression methods available through technology to interpret correlations Instruction 9781269614399 422 Linear Correlation




Review 9781269614399 490 Exercise 12e



(iv) use regression methods available through technology to make predictions Instruction 9781269614399 420 Activities 4 and 5




(i) formulate a meaningful question





(ii) determine the data needed to answer the question








(iii) gather the appropriate data





(iv) analyze the data





(v) draw reasonable conclusions








(i) communicate methods used for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation





(ii) communicate analyses conducted for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation





(iii) communicate conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation




Page 103 of 205 Pearson Education, Inc., publishing as Prentice Hall: 9781269614115 ELPS: Student Material


Knowledge and Skills Statement Student Expectation Breakout Required Grade Level Component ISBN Page (s) Specific Location

1) Cross-curricular second language acquisition/learning strategies. The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:

(A) use prior knowledge and experiences to understand meanings in English

(1) use prior knowledge to understand meanings in English

T: 9-12S: 9-12

9781269614115 80 Lesson 1.8

9781269614115 668 Lesson 5.119781269614115 709 Lesson 6.49781269614115 884 Lesson 7.4

9781269614115

The English language proficiency standards (ELPS) outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement the ELPS as an integral part of each subject in the required curriculum. This document outlines the ELPS that have been designated as appropriate for inclusion in instructional materials. Since the designated ELPS are included in student materials for English language arts and reading, the ELPS are not required to be included in Proclamation 2015 instructional materials for Kindergarten through grade 5 where students are typically taught in self-contained classroom settings rather than departmentalized classes. Additionally, many of the designated ELPS are most appropriate for inclusion in teacher materials and are only required to be included in student materials where specifically indicated.

(c) Cross-curricular second language acquisition essential knowledge and skills

Correlations to the English Language Proficiency Standards (ELPS): Student Material

Chapter 111. MathematicsSubchapter C. High School§111.43. Mathematical Models with Applications, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice HallMathematical Models with Applications, Texas Edition






(2) use prior experiences to understand meanings in English

T: 9-12S: 9-12

9781269614115 247 Lesson 2.8

9781269614115 451 Lesson 3.109781269614115 683 Lesson 6.1


(B) monitor oral and written language production and employ self-corrective techniques or other resources

(1) monitor oral language production and employ self-corrective techniques or other resources

T: 9-12



(2) monitor written language production and employ self-corrective techniques or other resources

NA





(C) use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary

(1) use strategic learning techniques to acquire basic and grade-level vocabulary

NA


(D) speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)

(1) speak using learning strategies

T: 9-12S: 9-12

9781269614115 2 Lesson 1.1

9781269614115 605 Lesson 5.29781269614115 805 Lesson 6.14


(E) internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment

(1) internalize new basic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA






(2) internalize new basic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA



(3) internalize new academic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA



(4) internalize new academic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA





(F) use accessible language and learn new and essential language in the process

(1) use accessible language and learn new and essential language in the process

T: 9-12


(G) demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one commensurate with grade-level learning expectations

(1) demonstrate an increasing ability to distinguish between formal and informal English

NA



(2) demonstrate an increasing knowledge of when to use [formal and informal English] commensurate with grade-level learning expectations

NA





(H) develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations

(1) develop and expand repertoire of learning strategies

NA

(2) Cross-curricular second language acquisition/listening. The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:

(A) distinguish sounds and intonation patterns of English with increasing ease

(1) distinguish sounds of English with increasing ease

NA



(2) distinguish intonation patterns of English with increasing ease

NA





(B) recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters

(1) recognize elements of the English sound system in newly acquired vocabulary

NA


(C) learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions

(1) learn new language structures heard during classroom instruction and interactions

T: 9-12



(2) learn new expressions heard during classroom instruction and interactions

T: 9-12






(3) learn basic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614115 211 Lesson 2.5

362 Lesson 3.1736 Lesson 6.6



(4) learn academic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614115 133 Lesson 1.13

9781269614115 362 Lesson 3.19781269614115 662 Lesson 5.10





(D) monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed

(1) monitor understanding of spoken language during classroom instruction and interactions

T: 9-12



(2) seek clarification [of spoken language] as needed

T: 9-12S: 9-12

9781269614115 502 Lesson 4.1

9781269614115 668 Lesson 5.119781269614115 821 Lesson 6.16





(E) use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language

(1) use visual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA



(2) use contextual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA



(3) use linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language

T: 9-12S: 9-12

9781269614115 133 Lesson 1.13




9781269614115 271 Lesson 2.119781269614115 631 Lesson 5.6


(F) listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment

(1) listen to and derive meaning from a variety of media to build and reinforce concept attainment

NA



(2) listen to and derive meaning from a variety of media to build and reinforce language attainment

NA





(G) understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar

(1) understand the general meaning of spoken language ranging from situations in which topics are familiar to unfamiliar

NA



(2) understand the general meaning of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(3) understand the general meaning of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA






(4) understand the main points of spoken language ranging from situations in which topics are familiar to unfamiliar

NA



(5) understand the main points of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(6) understand the main points of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA






(7) understand the important details of spoken language ranging from situations in which topics are familiar to unfamiliar

NA



(8) understand the important details of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(9) understand the important details of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA





(H) understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations

(1) understand implicit ideas in increasingly complex spoken language commensurate with grade-level learning expectations

NA



(2) understand information in increasingly complex spoken language commensurate with grade-level learning expectations

NA


(I) demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs

(1) demonstrate listening comprehension of increasingly complex spoken English by following directions commensurate with content and grade-level needs

NA






(2) demonstrate listening comprehension of increasingly complex spoken English by retelling or summarizing spoken messages commensurate with content and grade-level needs

NA



(3) demonstrate listening comprehension of increasingly complex spoken English by responding to questions and requests commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614115 447 Lesson 3.9

9781269614115 605 Lesson 5.29781269614115 890 Lesson 7.5






(4) demonstrate listening comprehension of increasingly complex spoken English by collaborating with peers commensurate with content and grade-level needs

T: 9-12



(5) demonstrate listening comprehension of increasingly complex spoken English by taking notes commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614115 110 Lesson 1.11

9781269614115 436 Lesson 3.89781269614115 871 Lesson 7.3




(3) Cross-curricular second language acquisition/speaking. The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:

(A) practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible

(1) practice producing sounds of newly acquired vocabulary to pronounce English words in a manner that is increasingly comprehensible

NA


(B) expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication

(1) expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects

NA






(2) expand and internalize initial English vocabulary by retelling simple stories and basic information represented or supported by pictures

NA



(3) expand and internalize initial English vocabulary by learning and using routine language needed for classroom communication

T: 9-12S: 9-12

9781269614115 102 Lesson 1.10






(C) speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired

(1) speak using a variety of grammatical structures with increasing accuracy and ease as more English is acquired

NA



(2) speak using a variety of sentence lengths with increasing accuracy and ease as more English is acquired

NA






(3) speak using a variety of sentence types with increasing accuracy and ease as more English is acquired

NA



(4) speak using a variety of connecting words with increasing accuracy and ease as more English is acquired

T: 9-12S: 9-12

9781269614115 23 Lesson 1.4






(D) speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency

(1) speak using grade-level content area vocabulary in context to internalize new English words

T: 9-12S: 9-12

9781269614115 6 Lesson 1.2




(2) speak using grade-level content area vocabulary in context to build academic language proficiency

T: 9-12S: 9-12

9781269614115 23 Lesson 1.4






(E) share information in cooperative learning interactions

(1) share information in cooperative learning interactions

T: 9-12S: 9-12

9781269614115 306 Lesson 2.14

9781269614115 641 Lesson 5.79781269614115 740 Lesson 6.79781269614115


(F) ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

(1) ask [for] information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614115 238 Lesson 2.7

9781269614115 570 Lesson 4.99781269614115 645 Lesson 5.8






(2) give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614115 92 Lesson 1.9



(G) express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

(1) express opinions ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12






(2) express ideas ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12



(3) express feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

NA





(H) narrate, describe, and explain with increasing specificity and detail as more English is acquired

(1) narrate with increasing specificity and detail as more English is acquired

NA



(2) describe with increasing specificity and detail as more English is acquired

NA






(3) explain with increasing specificity and detail as more English is acquired

T: 9-12S: 9-12

9781269614115 254 Lesson 2.9

9781269614115 709 Lesson 6.49781269614115 865 Lesson 7.2


(I) adapt spoken language appropriately for formal and informal purposes

(1) adapt spoken language appropriately for formal purposes

NA






(2) adapt spoken language appropriately for informal purposes

NA


(J) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment

(1) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept attainment

NA






(2) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce language attainment

N/A

(4) Cross-curricular second language acquisition/reading. The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For kindergarten and grade 1, certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:

(A) learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots and base words

(1) learn relationships between sounds and letters of the English language

NA






(2) decode (sound out) words using a combination of skills

NA


(B) recognize directionality of English reading such as left to right and top to bottom

(1) recognize directionality of English reading

NA





(C) develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials

(1) develop basic sight vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614115 186 Lesson 2.3

9781269614115 847 Lesson 7.19781269614115 944 Lesson 7.11



(2) derive meaning of environmental print

T: 9-12S: 9-12

9781269614115 55 Lesson 1.6

9781269614115 539 Lesson 4.69781269614115 645 Lesson 5.8






(3) comprehend English vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614115 392 Lesson 3.3

9781269614115 788 Lesson 6.129781269614115 934 Lesson 7.9



(4) comprehend English language structures used routinely in written classroom materials

T: 9-12S: 9-12

9781269614115 219 Lesson 2.6






(D) use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text

(1) use prereading supports to enhance comprehension of written text

T: 9-12S: 9-12

9781269614115 256 Lesson 2.10

9781269614115 617 Lesson 5.4


(E) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

(1) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

T: 9-12





(F) use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

(1) use visual and contextual support to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614115 422 Lesson 3.6

9781269614115 757 Lesson 6.89781269614115 903 Lesson 7.7



(2) use visual and contextual support to enhance and confirm understanding

T: 9-12S: 9-12

9781269614115 201 Lesson 2.4

9781269614115 784 Lesson 6.11






(3) use visual and contextual support to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614115 35 Lesson 1.5

9781269614115 722 Lesson 6.59781269614115 814 Lesson 6.15



(4) use visual and contextual support to develop grasp of language structures needed to comprehend increasingly challenging language

NA






(5) use visual and contextual support to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614115 169 Lesson 2.1




(6) use support from peers and teachers to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614115 509 Lesson 4.2

9781269614115 768 Lesson 6.10






(7) use support from peers and teachers to enhance and confirm understanding

T: 9-12S: 9-12

9781269614115 509 Lesson 4.2

9781269614115 768 Lesson 6.10



(8) use support from peers and teachers to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614115 410 Lesson 3.5

9781269614115 703 Lesson 6.39781269614115 903 Lesson 7.7






(9) use support from peers and teachers to develop grasp of language structures needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614115 313 Lesson 2.15

9781269614115 625 Lesson 5.59781269614115 925 Lesson 7.8



(10) use support from peers and teachers to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614115 283 Lesson 2.12

9781269614115 703 Lesson 6.39781269614115 821 Lesson 6.16





(G) demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

(1) demonstrate comprehension of increasingly complex English by participating in shared reading commensurate with content area and grade level needs

NA



(2) demonstrate comprehension of increasingly complex English by retelling or summarizing material commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614115 110 Lesson 1.11

9781269614115 323 Lesson 2.169781269614115 695 Lesson 6.2






(3) demonstrate comprehension of increasingly complex English by responding to questions commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614115 69 Lesson 1.7




(4) demonstrate comprehension of increasingly complex English by taking notes commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614115 10 Lesson 1.3

9781269614115 528 Lesson 4.49781269614115 896 Lesson 7.6





(H) read silently with increasing ease and comprehension for longer periods

(1) read silently with increasing ease for longer periods

NA



(2) read silently with increasing comprehension for longer periods

NA





(I) demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text and distinguishing main ideas from details commensurate with content area needs

(1) demonstrate English comprehension by employing basic reading skills commensurate with content area needs

NA



(2) expand reading skills commensurate with content area needs

NA





(J) demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs

(1) demonstrate English comprehension and expand reading skills by employing inferential skills

NA


(K) demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade level needs

(1) demonstrate English comprehension and expand reading skills by employing analytical skills

NA




(5) Cross-curricular second language acquisition/writing. The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For kindergarten and grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:

(A) learn relationships between sounds and letters of the English language to represent sounds when writing in English

(1) learn relationships between sounds and letters of the English language to represent sounds when writing in English

NA


(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary

(1) write using newly acquired basic vocabulary

NA






(2) write using content-based grade-level vocabulary

NA


(C) spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired

(1) spell familiar English words with increasing accuracy

NA






(2) employ English spelling pattern with increasing accuracy as more English is acquired

NA



(3) employ English spelling rules with increasing accuracy as more English is acquired

NA





(D) edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired

(1) edit writing for standard grammar and usage, including subject-verb agreement commensurate with grade-level expectations as more English is acquired

NA



(2) edit writing for standard grammar and usage, including pronoun agreement, commensurate with grade-level expectations as more English is acquired

NA






(3) edit writing for standard grammar and usage, including appropriate verb tenses, commensurate with grade-level expectations as more English is acquired

NA


(E) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations such as (i) using correct verbs, tenses, and pronouns/antecedents; (ii) using possessive case (apostrophe -s) correctly; and, (iii) using negatives and contractions correctly

(1) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations

NA





(F) write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired

(1) write using a variety of grade-appropriate sentence lengths in increasingly accurate ways as more English is acquired

NA



(2) write using a variety of grade-appropriate sentence patterns in increasingly accurate ways as more English is acquired

NA






(3) write using a variety of grade-appropriate connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired

NA


(G) narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

(1) narrate with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA






(2) describe with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA



(3) explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA


Page 154 of 205 Pearson Education, Inc., publishing as Prentice Hall: 9781269614115 ELPS: Teacher Material





(1) use prior knowledge to understand meanings in English

T: 9-12S: 9-12

9781269614399 1b Lesson 1.5

9781269614115

The English language proficiency standards (ELPS) outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement the ELPS as an integral part of each subject in the required curriculum. This document outlines the ELPS that have been designated as appropriate for inclusion in instructional materials. Since the designated ELPS are included in student materials for English language arts and reading, the ELPS are not required to be included in Proclamation 2015 instructional materials for Kindergarten through grade 5 where students are typically taught in self-contained classroom settings rather than departmentalized classes. Additionally, many of the designated ELPS are most appropriate for inclusion in teacher materials and are only required to be included in student materials where specifically indicated.

(c) Cross-curricular second language acquisition essential knowledge and skills

Correlations to the English Language Proficiency Standards (ELPS): Teacher Material

Chapter 111. MathematicsSubchapter C. High School§111.43. Mathematical Models with Applications, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice HallMathematical Models with Applications, Texas Edition






(2) use prior experiences to understand meanings in English

T: 9-12S: 9-12

9781269614399 1b Lesson 1.3



(1) monitor oral language production and employ self-corrective techniques or other resources

T: 9-12

9781269614399 359b Lesson 3.8



(2) monitor written language production and employ self-corrective techniques or other resources

NA





(C) use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary

(1) use strategic learning techniques to acquire basic and grade-level vocabulary

NA


(D) speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)

(1) speak using learning strategies

T: 9-12S: 9-12

9781269614399 359b Lesson 3.8



(1) internalize new basic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA






(2) internalize new basic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA



(3) internalize new academic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA



(4) internalize new academic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA





(F) use accessible language and learn new and essential language in the process

(1) use accessible language and learn new and essential language in the process

T: 9-12

9781269614399 497b Lesson 4.4



(1) demonstrate an increasing ability to distinguish between formal and informal English

NA



(2) demonstrate an increasing knowledge of when to use [formal and informal English] commensurate with grade-level learning expectations

NA





(H) develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations

(1) develop and expand repertoire of learning strategies

NA



(1) distinguish sounds of English with increasing ease

NA



(2) distinguish intonation patterns of English with increasing ease

NA





(B) recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters

(1) recognize elements of the English sound system in newly acquired vocabulary

NA



(1) learn new language structures heard during classroom instruction and interactions

T: 9-12

9781269614399 1b Lesson 1.3






(2) learn new expressions heard during classroom instruction and interactions

T: 9-12

9781269614399 169b Lesson 2.2



(3) learn basic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614399 497b Lesson 4.7






(4) learn academic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614399 497b Lesson 4.9



(1) monitor understanding of spoken language during classroom instruction and interactions

T: 9-12

9781269614399 497b Lesson 4.9






(2) seek clarification [of spoken language] as needed

T: 9-12S: 9-12

9781269614399 497b Lesson 4.9



(1) use visual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA






(2) use contextual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA



(3) use linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language

T: 9-12S: 9-12

9781269614399 683b Lesson 6.6






(1) listen to and derive meaning from a variety of media to build and reinforce concept attainment

NA



(2) listen to and derive meaning from a variety of media to build and reinforce language attainment

NA



(1) understand the general meaning of spoken language ranging from situations in which topics are familiar to unfamiliar

NA






(2) understand the general meaning of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(3) understand the general meaning of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA



(4) understand the main points of spoken language ranging from situations in which topics are familiar to unfamiliar

NA






(5) understand the main points of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(6) understand the main points of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA



(7) understand the important details of spoken language ranging from situations in which topics are familiar to unfamiliar

NA






(8) understand the important details of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(9) understand the important details of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA



(1) understand implicit ideas in increasingly complex spoken language commensurate with grade-level learning expectations

NA






(2) understand information in increasingly complex spoken language commensurate with grade-level learning expectations

NA



(1) demonstrate listening comprehension of increasingly complex spoken English by following directions commensurate with content and grade-level needs

NA



(2) demonstrate listening comprehension of increasingly complex spoken English by retelling or summarizing spoken messages commensurate with content and grade-level needs

NA






(3) demonstrate listening comprehension of increasingly complex spoken English by responding to questions and requests commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614399 359b Lesson 3.6



(4) demonstrate listening comprehension of increasingly complex spoken English by collaborating with peers commensurate with content and grade-level needs

T: 9-12

9781269614399 359b Lesson 3.6






(5) demonstrate listening comprehension of increasingly complex spoken English by taking notes commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614399 497b Lesson 4.4


(A) practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible

(1) practice producing sounds of newly acquired vocabulary to pronounce English words in a manner that is increasingly comprehensible

NA






(1) expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects

NA



(2) expand and internalize initial English vocabulary by retelling simple stories and basic information represented or supported by pictures

NA






(3) expand and internalize initial English vocabulary by learning and using routine language needed for classroom communication

T: 9-12S: 9-12

9781269614399 599b Lesson 5.11



(1) speak using a variety of grammatical structures with increasing accuracy and ease as more English is acquired

NA






(2) speak using a variety of sentence lengths with increasing accuracy and ease as more English is acquired

NA



(3) speak using a variety of sentence types with increasing accuracy and ease as more English is acquired

NA






(4) speak using a variety of connecting words with increasing accuracy and ease as more English is acquired

T: 9-12S: 9-12

9781269614399 847b Lesson 7.2



(1) speak using grade-level content area vocabulary in context to internalize new English words

T: 9-12S: 9-12

9781269614399 497b Lesson 4.7






(2) speak using grade-level content area vocabulary in context to build academic language proficiency

T: 9-12S: 9-12

9781269614399 497b Lesson 4.9


(E) share information in cooperative learning interactions

(1) share information in cooperative learning interactions

T: 9-12S: 9-12

9781269614399 497b Lesson 4.9






(1) ask [for] information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614399 169b Lesson 2.2



(2) give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614399 169b Lesson 2.2






(1) express opinions ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12

9781269614399 683b Lesson 6.5



(2) express ideas ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12

9781269614399 169b Lesson 2.13






(3) express feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

NA



(1) narrate with increasing specificity and detail as more English is acquired

NA






(2) describe with increasing specificity and detail as more English is acquired

NA



(3) explain with increasing specificity and detail as more English is acquired

T: 9-12S: 9-12

9781269614399 847b Lesson 7.2






(1) adapt spoken language appropriately for formal purposes

NA



(2) adapt spoken language appropriately for informal purposes

NA






(1) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept attainment

NA



(2) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce language attainment

N/A






(1) learn relationships between sounds and letters of the English language

NA



(2) decode (sound out) words using a combination of skills

NA





(B) recognize directionality of English reading such as left to right and top to bottom

(1) recognize directionality of English reading

NA



(1) develop basic sight vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614399 847b Lesson 7.1






(2) derive meaning of environmental print

T: 9-12S: 9-12

9781269614399 599b Lesson 5.5



(3) comprehend English vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614399 169b Lesson 2.13

9781269614399 847b Lesson 7.7






(4) comprehend English language structures used routinely in written classroom materials

T: 9-12S: 9-12

9781269614399 169b Lesson 2.13


(D) use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text

(1) use prereading supports to enhance comprehension of written text

T: 9-12S: 9-12

9781269614399 1b Lesson 1.13





(E) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

(1) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

T: 9-12

9781269614399 359b Lesson 3.2



(1) use visual and contextual support to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614399 359b Lesson 3.2






(2) use visual and contextual support to enhance and confirm understanding

T: 9-12S: 9-12

9781269614399 1b Lesson 1.13



(3) use visual and contextual support to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614399 359b Lesson 3.8

9781269614399 847b Lesson 7.7






(4) use visual and contextual support to develop grasp of language structures needed to comprehend increasingly challenging language

NA



(5) use visual and contextual support to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614399 1b Lesson 1.5

9781269614399 599b Lesson 5.11






(6) use support from peers and teachers to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614399 683 Lesson 6.5



(7) use support from peers and teachers to enhance and confirm understanding

T: 9-12S: 9-12

9781269614399 497b Lesson 4.7

9781269614399 599b Lesson 5.11






(8) use support from peers and teachers to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614399 683b Lesson 6.6



(9) use support from peers and teachers to develop grasp of language structures needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614399 1b Lesson 1.3






(10) use support from peers and teachers to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614399 1b Lesson 1.5



(1) demonstrate comprehension of increasingly complex English by participating in shared reading commensurate with content area and grade level needs

NA






(2) demonstrate comprehension of increasingly complex English by retelling or summarizing material commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614399 497b Lesson 4.4

9781269614399 599b Lesson 5.7



(3) demonstrate comprehension of increasingly complex English by responding to questions commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614399 497b Lesson 4.7

9781269614399 599b Lesson 5.7






(4) demonstrate comprehension of increasingly complex English by taking notes commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614399 683b Lesson 6.15



(1) read silently with increasing ease for longer periods

NA






(2) read silently with increasing comprehension for longer periods

NA



(1) demonstrate English comprehension by employing basic reading skills commensurate with content area needs

NA






(2) expand reading skills commensurate with content area needs

NA


(J) demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs

(1) demonstrate English comprehension and expand reading skills by employing inferential skills

NA





(K) demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade level needs

(1) demonstrate English comprehension and expand reading skills by employing analytical skills

NA


(A) learn relationships between sounds and letters of the English language to represent sounds when writing in English

(1) learn relationships between sounds and letters of the English language to represent sounds when writing in English

NA






(1) write using newly acquired basic vocabulary

NA



(2) write using content-based grade-level vocabulary

NA






(1) spell familiar English words with increasing accuracy

NA



(2) employ English spelling pattern with increasing accuracy as more English is acquired

NA






(3) employ English spelling rules with increasing accuracy as more English is acquired

NA



(1) edit writing for standard grammar and usage, including subject-verb agreement commensurate with grade-level expectations as more English is acquired

NA






(2) edit writing for standard grammar and usage, including pronoun agreement, commensurate with grade-level expectations as more English is acquired

NA



(3) edit writing for standard grammar and usage, including appropriate verb tenses, commensurate with grade-level expectations as more English is acquired

NA





(E) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations such as (i) using correct verbs, tenses, and pronouns/antecedents; (ii) using possessive case (apostrophe -s) correctly; and, (iii) using negatives and contractions correctly

(1) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations

NA



(1) write using a variety of grade-appropriate sentence lengths in increasingly accurate ways as more English is acquired

NA






(2) write using a variety of grade-appropriate sentence patterns in increasingly accurate ways as more English is acquired

NA



(3) write using a variety of grade-appropriate connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired

NA






(1) narrate with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA



(2) describe with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA






(3) explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA

a correlation of mathematical models - pearson...

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